It is shown that the well-known empirical exponential bias-dependent mobility is an approximation function of the relevant term emerging in the Mott-Gurney space charge limited current model when the constant non-zero electric field at the hole injecting metal/organic interface E-int is taken into account. The term in question is the product of the bias-independent (but organic layer thickness-dependent) effective mobility coefficient and the algebraic function, f(lambda), of the argument lambda = E-int/E-a, where E-a is the externally applied electric field. On account of the non-zero interfacial field, E-int, the singularity of the spatial dependence of the hole current density, p(x), is removed. The resulting hole drift current density, j, is tested as a function of E-a against a number of published room temperature hole current j-E-a data sets, all characterized by good ohmic contact at the hole injecting interface. It is shown that the calculated current density provides a very good fit to the measurements within a high range of E-a intervals. Low values of E-a, are investigated analytically under the assumption of hole drift-diffusion. The extremely large internal electric fields at the anode/organic junction indicate drift-diffusion to be an improbable process for the structures investigated. However, a description of hole transport throughout the whole interval of experimental E-a values may be obtained at low values of E-a by an extended Mark-Helfrich drift model with traps occupying the exponentially distributed energy levels, followed by the extended Mott-Gurney model description within the remaining part of the E-a interval. In both models the same (bias-independent) effective mobility coefficient is incorporated into the calculations. The results present evidence that within the framework of the extended Mott-Gurney expression the properly derived term should replace the empirical exponential bias-dependent mobility, making it redundant in the interpretation of j-V data. (C) 2014 Elsevier B.V. All rights reserved.